9514 1404 393
Answer:
12.25 (or -18.75)
Explanation:
If you pay attention to the square of a binomial, ...
(x -a)² = x² -2ax +a²
You see that the constant (a²) is the square of half the x-coefficient. That is, the x-coefficient is -2a, half that is -a, and the square of that is (-a)² = a².
In your equation, the x-coefficient is -7, half that is -3.5, and the square of that is 3.5² = 12.25.
So, you can think of this ambiguous question in a couple of ways.
Concern is only with the x-terms:
x² -7x +31 = (x² -7x +12.25) +31 = 12.25 . . . . . . add 12.25 to both sides
(x -3.5)² +31 = 12.25 . . . . write the x-terms as a square
Concern with the equation overall:
You want the end result to have the x-terms in the form of the square ...
(x -3.5)² = x -7x +12.25
The left side of the equation can be put in that form by adding -18.75 to both sides;
x² -7x +31 -18.75 = -18.75 . . . . . . add -18.75 to both sides
x² -7x +12.25 = -18.75 . . . . . . . . . simplify
(x -3.5)² = -18.75 . . . . . . write the left side as a square
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The short of it is that we're not sure what the question is asking for exactly. The "help video" would probably clarify the intent. Most likely, you're concerned with adding the square of half the x-coefficient, 12.25.